Journal of New Technology and Materials
JNTM
OEB Univ. Publish. Co.
Vol. 04, N°01 (2014)35-38
Electrical characteristics of Organic Light Emitting Diode
“OLED” finite difference modeling
Benatia Khaoula 1* and Telia Azzedine 1
1
Instrumentation and Microsystems Laboratory (LMI), Constantine 1 University, route Ein El Bey, Constantine
25000 , Algeria
*Corresponding author: [email protected]
Received: 30 April 2014, accepted 26 May 2014
Abstract
In this paper, a finite difference modeling of single layer organic light emitting diode “OLED” based on MEH-PPV [Poly (2Methoxy, 5-(2’-Ethyl-Hexoxy)-1, 4-Phenylene-Vinylene)] and DP-PPV [Poly (2, 3-DiPhenyl-Phenylene-Vinylene)] is presented
through the simulation of the basic equations i.e. the time independent continuity equations, with a drift diffusion form for
current density, coupled to Poisson’s equation. Thus, several parameters are extracted from this model; J (V) characteristics for
the two devices which are compared to the experimental results and the spatial distributions of the potential, the electric field
and the carrier concentrations.
Keywords: OLED; simulation ; finite difference;MEH-PPV; DP-PPV; J(V) characteristics
In this paper, we present the model that we worked
on along with the boundary conditions where a set of
equations were solved using finite difference method.
Simulation results of J (V) characteristics for different
organic semiconductor materials and for various
thicknesses were compared to experimental data from
, a spatial distribution of carrier density, potential
and electric field are shown.
[3]
1. Introduction
Organic light emitting devices have been
remarkably improved since the announcement of the
first Organic light emitting diode “OLED” in 1987 .
These organic devices have a great potential indeed in
various industries as are used in many applications
such as lighting, handheld displays like smart phones,
tablets and cameras and TV’s of course. Even though
this great development, OLED’s are still lacking in
some other areas related to the lifetime of these
devices, the injection and transport mechanism which
are not properly determined since the organic
semiconductors have an amorphous structure unlike
the inorganic ones that present a crystallized one.
To understand the operation principle of such
devices, and before manufacturing them, we have to
predict first their behavior by studying them trough
what we know now as “Numerical modeling” , which
is a powerful method of visualizing the dynamic
behavior of physical systems of such devices. In this
respect, we used an electrical model composed of
Poisson’s equation, coupled to the time independent
continuity equations, with a drift diffusion form for the
current density.
[1]
[2]
[4, 5]
2. The device model
In this section, the electrical model is presented
along with the boundary conditions; finite difference
method was applied to solve the basic equations and
Gummel iteration is used
[6].
2.1. Governing equations
To fully understand the mechanism of the
transport and the injection of electrons /holes, we use
the inorganic semiconductor devices equations i.e. the
time independent continuity equations, with a drift
diffusion form for current density, coupled to
Poisson’s equation, for modeling the organic
semiconductor based devices as follows:
∂J n
∂x
= G − R;
∂Jp
∂x
= G − R,
(𝟏)
Electrical characteristics of Organic Light Emitting Diode…
Jn (Jp ) is the electron (hole) current density, G is the
carrier generation rate which is very small for materials
with an energy gap larger than 2 eV, and R is the
carrier recombination rate, this latter is not that
important for the single carrier structures . In the
following expressions of Jn and Jp , the diffusivities are
dependent of the mobilities using Einstein relation.
𝐧𝟎 = Nc exp −
𝐧𝐋 = Nc exp −
[4]
Jn = q μn n. E +
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𝐩𝟎 = Nv exp −
k B T ∂n
;
q ∂x
𝐩𝐋 = Nv exp −
k B T ∂p
Jp = q μp p. − q ∂x
Kh. Benatia et al.
ϕb1
,
kB T
E g −ϕ b 1
kB T
ϕb2
,
kB T
(𝟖)
E g −ϕ b 2
kB T
Where 𝐍𝐜 and 𝐍𝐯 are assumed to be equal and
correspond to the density of negatively and positively
chargeable sites in the film, 𝐄𝐠 the band gap energy,
𝛟𝐛𝟏 (𝛟𝐛𝟐 ) is the electron (hole) energy barrier.
(𝟐)
Where 𝐪 is the electronic charge, 𝐧(𝐩) is the electron
(hole) density, 𝐄 is the electric field, 𝐤 𝐁 is Boltzmann’s
constant, 𝐓 is the temperature and, 𝛍𝐧 (𝛍𝐩 ) is the
electron (hole) mobility which is expected to be PooleFrenkel electric field dependent:
The following expressions of the three main
equations; (1), (2) and (5) are obtained using the finite
difference method :
[7]
Poisson’s equation:
μPF
qεa
qβ
= μ0 exp −
exp
kT
kT
E
(𝟑)
Vi+1 + Vi−1 − 2Vi =
Where 𝛍𝟎 is the temperature independent pre-factor
mobility, 𝛆𝐚 is the thermal activation energy and 𝛃 is
the Poole-Frenkel factor.
(𝟗)
Coupled continuity and drift-diffusion equations:
− Vi+1 − Vi + VT ni+1 + Vi − Vi−1
+ VT ni−1 = 0
Poisson’s equation is:
dE
q
=
p − n + ND − NA
dx
ε
h2 q
ni − pi + Na − ND
ε
− 2VT ni
− Vi+1 − Vi − VT pi+1 + Vi − Vi−1 + 2VT pi
− VT pi−1 = 0
(𝟏𝟎)
(𝟒)
The electrostatic potential 𝐕 is related to𝐄 by:
dV
E=−
(𝟓)
dx
Where 𝛆 is the static dielectric constant, 𝐍𝐃 is the
donor density and 𝐍𝐀 is the acceptor one.
2.2. Boundary conditions
Considering the boundary conditions for the
potential:
V(0) = 0,
V L = Vd − Va
3. Results and discussions
Fig.1 shows the band diagram of the device, where
we consider a single layer organic diode based on:
first: MEH-PPV [Poly (2-Methoxy, 5-(2’-EthylHexoxy)-1, 4-Phenylene-Vinylene)], taking into
account the electron and hole energy levels E =
𝟐. 𝟖 𝐞𝐕 and E = 𝟓. 𝟑 𝐞𝐕, with the dielectric constant
Ɛ = 𝟑 and n = 𝟏𝟎𝟐𝟏 𝐂𝐦−𝟑 . The organic layer is
sandwiched between the anode ITO (Indium Tin
Oxide) and the cathode Cu. The barrier for electron
injection is 1.9 eV and for hole injection is 0.2 eV.
Second: DP-PPV with the electron and hole energy
levels E = 𝟐. 𝟗𝟒 𝐞𝐕 and E = 𝟓. 𝟔𝟔 𝐞𝐕, with the
(𝟔)
Where 𝐕𝐚 (𝐕𝐝 ) is the application (diffusion) potential.
c
The diffusion potential is expressed as:
v
Vd =
kB T
q
ln
nL
n0
= −
kB T
q
ln
pL
p0
r
(𝟕)
The equilibrium free carrier concentrations at the
interfaces are :
[3]
0
c
36
v
Electrical characteristics of Organic Light Emitting Diode…
dielectric constant Ɛ = 𝟑 and n = 𝟏𝟎𝟐𝟏 𝐂𝐦−𝟑 . The
organic layer is sandwiched between the anode ITO
and PEDOT:PSS [Poly (3,4-Ethylene Dioxy
Thiophene): Poly(Styrene Sulphonate)], and the
cathode Ca. The barrier for electron injection is 0.04
eV and for hole injection is 0.46 eV.
r
JNTM(2014)
Kh. Benatia et al.
0
Fig.2 and Fig.3 present the spatial distribution of
the potential and the electric field respectively for
ITO/MEH-PPV/Cu device with a thickness of
45.7
nm.
Fig.4 shows the spatial distribution of the carriers
density for both holes and electrons where the density
of holes is much greater compared to electrons. In
fact, the holes barrier injection is too small that these
carriers pass through this barrier, in the opposite of
the electrons where only few of them can traverse
through this barrier.
Using this model, we can also calculate the J-V
characteristics for ITO/MEH-PPV/Cu device for
different thicknesses where these results shown in
Fig.5, Fig.6, and Fig.7 are compared with experimental
ones from .
[4]
37
Electrical characteristics of Organic Light Emitting Diode…
JNTM(2014)
Kh. Benatia et al.
We applied the model used previously on
PEDOT: PSS/DP-PPV/Ca device. Fig.8 shows a
comparison of calculated and measured J-V
characteristics of a 50-nm- thick DP-PPV diode .
[5]
4. Conclusion
In this study, finite difference method was applied
for modeling the basic equations that control the
operation principle of an OLED. The hole density is
much greater than that of the electrons. From the J-V
characteristics, the turn-on voltage increase with the
thickness of the polymer layer and in the two devices
based on MEH-PPV and DP-PPV, the same behavior
was noticed and a shift between the experimental data
and the calculated results was observed.
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